Understanding the inter-relationships among addiction to multiple drugs and between co-occurring substance use and psychiatric disorders is a key priority of NIDA's, given ample research showing extremely high rates of their co-morbidity. Limitations of existing analytic methods impede further progress in these areas, because trajectories describing drug use and co-occurring disorders over time are complex--often nonlinear and based on outcomes with different distributions. Timeline Follow back (TLFB), the most widely utilized and accepted measure for determining drug use outcomes, collects reports of daily use (e.g. used marijuana, yes/no; joints per day) on multiple drugs over specified intervals. But TLFB data are not analyzed as collected (e.g. repeated binomial and Poisson variables). Rather, data are typically collapsed into summaries like total days of use (or abstinence) during a trial, or collapsed over smaller intervals (e.g. monthly sums of days used) in an attempt to create normally distributed variables. Such composite scores sacrifice information, lose efficiency, and are often not normal. Abundant previously collected longitudinal data on outcomes with different distributions like those from TLFB exist, but an inability to analyze them as such prevents satisfactorily addressing scientifically and clinically relevant questions such as: What is the temporal relationship between use of two or more drugs? What is the temporal relationship between change in drug use and change in co-occurring disorders? Do co- occurring psychiatric symptoms remit with reductions in drug use, or do reductions in psychiatric symptoms precede reductions in drug use? At what point does reduction in one occur relative to the other? This project's first two aims propose rigorous theoretical derivation and simulation to develop a multivariate nonlinear mixed model (MvNLMIXED) to simultaneously estimate and compare nonlinear trajectories of substance use and comorbidity outcomes with different distributions over time and between groups (Aim 1), and to evaluate inter- relationships among those jointly modeled trajectories by estimating their association (Aim 2a) and the order of, and time-lag among, change in one relative to the other (Aim 2b). Aims 3 and 4 will apply MvNLMIXED methods to answer important questions in two pharmacotherapy trials for co-occurring Attention-Deficit Hyperactivity Disorder (ADHD) in adolescents who also received cognitive behavioral therapy for drug use: a trial of atomoxetine and a multi-site trial o Osmotic-Release Methylphenidate in NIDA's Clinical Trials Network. These novel analyses are expected to identify important inter-relationships among use of different drugs with each other (Aim 3) and with ADHD (Aim 4), potentially informing how treatment may be operating. Beyond their importance for evaluating inter-relationships in these two trials and among drug use and comorbidity in general, these novel methods are widely applicable to evaluating temporal relationships among any jointly modeled longitudinal variables, benefiting new research and enhancing the scientific value of existing databases. User-friendly software for these methods will be made available on multiple platforms.